Question

Let z = 1 + 3i and w = -3 - 4i.
Use the drop down menus to complete the statements.
The sum z + w is equal to - -i
The sum w + z is equal to - 2 - i
The result supports that complex number addition is

Answer 1

Step-by-step explanation:

z+w= 1+3i-3-4i = -2-i

w+z=-3-4i+1+3i = -2-i

So, z+w = w+z

So, complex number addition is commutative

Answer 2

If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

What is commutativity property of addition?

We are aware that the addition's commutative property states that altering the addends' order will not affect the sum.

How to solve it ?

Here z = 1 + 3i and w = -3 - 4i.

Now, z + w = 1 + 3i - 3 - 4i = 1 - 3 + 3i - 4i = - 2 - i

and w + z = - 3 - 4i + 1 + 3i = - 3 + 1 - 4i + 3i = - 2 - i

i.e. z + w = w + z

Clearly, the addition obeys the commutative property.

Therefore we can conclude that If z = 1 + 3i and w = -3 - 4i, then z + w = - 2 - i and w + z = - 2 - i, which supports that complex number addition is commutative.

Learn more about the commutative property here -

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